论文标题
一种关系方法，用于矩形，简单复合物和有限封闭
A Relational Approach to Matroids, Simplicial Complexes and Finite Closures
论文作者
论文摘要
主要结果是定理MAT 11，该定理MAT 11指出，每个有限闭合操作员都是矩阵的接地组。它的基础集由闭合的非冗余盖组成。这些是最小的子集，可以使用关系数据库理论的封闭算法来确定关闭操作员。对于每个世袭系列，都有一个平坦的封闭，可以定义一个矩形或简单络合物，但是每个闭合都定义了一个遗传收藏集，即数据库理论中的钥匙。 Maier的标准化算法是本文的基础。这是他的发展之后，并引用了他的相关结果来帮助阅读他的原始作品。本文的主要目的是将数据库理论的重要性引入所有有限闭合的分析，包括Matroid的扁平封闭。
The main result is Theorem MAT 11 which states that every finite closure operator is the ground set of a matroid. Its base sets consist of nonredundant covers of of the closure. These are minimal subsets that determine the closure operator using a closure algorithm from the theory of relational databases. For each hereditary collection there is one flat closure that define a matroid or simplicial complexes, but every closure defines a hereditary collection, its keys in database theory. The normalization algorithm by Maier is the basis of this paper. This follows his development, and his relevant results are cited to aid reading his original work. The main purpose of this paper is to introduce the importance of database theory into the analysis of all finite closure including the flat closures of matroids.
